A global urban microwave backscatter time series data set for 1993–2020 using ERS, QuikSCAT, and ASCAT data

Urban settlements are rapidly growing outward and upward, with consequences for resource use, greenhouse gas emissions, and ecosystem and public health, but rates of change are uneven around the world. Understanding trajectories and predicting consequences of global urban expansion requires quantifying rates of change with consistent, well-calibrated data. Microwave backscatter data provides important information on upward urban growth – essentially the vertical built-up area. We developed a multi-sensor, multi-decadal, gridded (0.05° lat/lon) data set of global urban microwave backscatter, 1993–2020. Comparison of backscatter from two C-band sensors (ERS and ASCAT) and one Ku-band sensor (QuikSCAT) are made at four invariant non-urban sites (~3500 km2) to evaluate instrument stability and multi-decadal pattern. For urban areas, there was a strong linear correlation (overall R2 = 0.69) between 2015 ASCAT urban backscatter and a continental-scale gridded product of building volume, across 8450 urban grid cells (0.05° × 0.05°) in Europe, China, and the USA. This urban backscatter data set provides a time series characterizing global urban change over the past three decades.


Methods
Microwave backscatter data. We selected images from three backscatter data collections with quasi-decadal data time series that have been processed by and are available from the NASA Scatterometer Climate Record Pathfinder (SCP) project (https://www.scp.byu.edu/). These collections are: ERS-1/2 25 , SeaWinds on QuikSCAT 26 , and Enhanced Resolution ASCAT 27 (Table 1). QuikSCAT is a Ku-band scatterometer (13.6 GHz) with rotating inner (HH polarization) and outer (VV polarization) pencil beam antennas, while ERS-1/2 and ASCAT-A/B are C-band scatterometers (5.3 GHz) with fixed swath VV antennas. C-and Ku-band microwaves have inherently different backscatter strengths from most land surfaces 20 . Calibration of the ASCAT sensors is good enough that multiple ASCAT instruments can be treated as a single sensor. ERS-1/2 are similarly well calibrated against each other and we combine these into a single time series.
The backscatter images are multi-day composites made from the original L1B data for individual passes, and are created using the Scatterometer Image Reconstruction (SIR) algorithm 28,29 . The image data are separated by geographical region, each with it's own Lambert Azimuthal Equal Area (LAEA) projection. The following regions were used: Alaska (Ala); Australia (Aus); Bering Sea (Ber); Central America (CAm); China/Japan (ChJ); Europe (Eur); Greenland (Grn); Indonesia (Ind); North Africa (NAf); North America (NAm); South Africa (SAf); South America (SAm); South Asia (SAs); and Siberia (Sib).  1 Schematic overview of the urban backscatter data sets. Shaded bars represent range of sensor data (see Methods) and solid circles represent summer season means for each year for ERS (1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000), QuikSCAT (1999QuikSCAT ( -2009, ASCAT (2007ASCAT ( -2020. Urban data domain masks: 0.05° lat/lon gridded backscatter data were masked by open water minimum threshold of 50%, and GHSL (Global Human Settlement Layer) 2014 builtfraction minimum threshold of 20%. ASCAT 2015 urban backscatter is compared to gridded building volume and height data for Europe, China, and the USA. www.nature.com/scientificdata www.nature.com/scientificdata/ As discussed in Long (2017) 29 , the SIR algorithm provides higher effective resolution than simple gridding algorithms by exploiting the overlapping spatial response function of the measurements to reconstruct the backscatter on a fine resolution grid. The grid size is smaller than the effective resolution ( Table 1) to ensure that Nyquist sampling requirements are met. Like all imaging techniques, the spatial response function of the image pixels extends somewhat beyond the pixel size, but falls to negligible values within one or two pixels. We note that the reconstruction acts as a high pass filter to enhance fine details and sharpens image edge. This can lead to Gibbs phenomena overshoot at edges 29 . Note that the re-projection and resampling for this data set reduces these negative effects. The images are available from the BYU site in '.sir' format, and we downloaded the "a" (σ°), as well as the associated land mask images for each region. QuikSCAT VV polarization data were chosen to be consistent with VV polarization C-band data. Note that the SCP "a" values for ERS and ASCAT are σ° at 40° incidence angle computed as σ°(dB) = a + b·(incidence_angle -40°). The images were converted to geotiff format (with data type = Float) and during the conversion to geotiff format the land mask for each region was applied.
The geotiffs generated from the multi-day .sir images (Table 1) were temporally aggregated for all three sensors both to monthly and to quarterly or "seasonal" (Jan-Mar, Apr-Jun, Jul-Sep, Oct-Dec) mean and standard deviation values. These seasonal values for σ° (in dB) were generated for the entire record for each instrument and for each region.
The data were assembled at 0.05° lat/lon spatial resolution, both for ease of use by a diverse community of researchers, and to be roughly consistent with the spatial resolution of the backscatter data processed and posted by the NASA SCP. We used the GDAL utility, gdalwarp, with the "average" resampling method to reproject the regional images to a lat-lon grid (EPSG:4326) then mosaicked the regions using the gdal_merge.py utility. This procedure results in a near global (58°S to 64.5°N) single image for each month or season. These images were assembled into NetCDF format files for each instrument with seasonal mean, seasonal standard deviation for both urban masked and unmasked (all land) data, and monthly mean and standard deviation for unmasked data.
A full analysis of the uncertainties associated with the backscatter measurements has already been provided in Long (2017) 29 . Extensive information and resources for understanding the uncertainties associated with the image reconstruction are available on the NASA SCP site (https://www.scp.byu.edu/). The standard deviation values that are part of this dataset are an estimate of the variability of the temporal aggregations to generate the monthly and seasonal values.
Additional data to constrain urban spatial domain. To mask the backscatter data to urban land, the GHSL built fraction (BF) in epoch 2014 30 was used to identify urban grid cells at 0.05° × 0.05°. We used the 1-km GHSL product (https://ghsl.jrc.ec.europa.eu/ghs_bu2019.php), which was developed from Landsat data 31,32 . The global gridded built fraction data (GHS-BUILT R2018A) were aggregated to 0.05° using the GDAL utility, gdalwarp, using the 'average' resampling method, equivalent to what was used with the backscatter data. A minimum built fraction threshold of 20% in 2014 was used to classify urban grid cells, following earlier work by Mahtta et al. 2 and consistent with a comparison of ASCAT and Sentinel-1 SAR data for Nanjing, China 33 . This 2014 built-fraction threshold was applied to all sensors and years, i.e., 1993-2020. Using the most recent (2014) urban cover data from GHSL maximizes the area classified as urban, including land urbanized in the 1990s and 2000s. We explore the sensitivity of this threshold in the figures below by also using a 10% built fraction threshold.
Because σ° values are very sensitive to water surfaces, and because many urban areas are located near water bodies, for the urban-masked data we applied an additional mask based on the water fraction in each grid cell. Grid cell water fraction was extracted from the Global 1-km Consensus Land Cover dataset 34 available at http:// www.earthenv.org//landcover. This was aggregated to 0.05° using the same method as for the urban built fraction, and for the urban data set, all 0.05° grid cells with water area >50% were excluded. Backscatter variance increased with increasing grid cell water fraction (e.g., coastal grid cells), and inspection of Shanghai, China at the mouth of the Yangtze River was used to select a threshold of 50%.
The combination of these two masks reduced our dataset from approximately 5.2 million grid cells (land) to 38,525 (urban) 0.05° × 0.05° grid cells. Note that the posted data also include unmasked (land) monthly and seasonal backscatter data sets, so that users can apply other masks to the data.

Data Records
The data set comprises eighteen NetCDF files at 0.05° (lat/lon) grid resolution. Six files are monthly mean backscatter time series, and backscatter standard deviation time series, for three sensors and eras: ERS (Jan 1993 -Dec www.nature.com/scientificdata www.nature.com/scientificdata/ Repository: Socioeconomic Data and Applications Center (SEDAC) 35 ; https://doi.org/10.7927/ gr2e-dh86. Note that SEDAC requires user registration and login to access data.

Technical Validation
In our analyses below, we used the backscatter power return ratio, PR = 10^(σ°/10), where σ° is the backscatter in dB, as reported in the datasets. Backscatter PR had a stronger linear correlation with independent building volume and height data than did σ° (see Summer ASCAT Backscatter Compared to Building Data below). For application to urbanization trends, it is important to minimize variability introduced by transient events (i.e., not related to the image reconstruction) that affect backscatter returns, such as weather (precipitation, floods, and fall/winter/spring freeze-thaw signals), and substantial variation in vegetation canopy reflectance. For this reason, we constructed an annual time series using three-month seasonal mean backscatter values during the growing season, i.e., Jul-Sep in the northern hemisphere, and Jan-Mar in the southern hemisphere. We acknowledge that the onset and duration of 'summer' varies across the globe, and may not even be well-defined in some parts of the tropics; our goal was not to capture a 'summer' effect, but only to minimize variability in a multi-year time series by selecting a fixed time domain with low probability of freeze-thaw and a fairly stable vegetation canopy from one year to the next (see further discussion below in Usage Notes). To illustrate a continuous backscatter time series for these three instruments, we developed a simple intercalibration of the summer mean backscatter time series -a constant offset of the QuikSCAT backscatter PR data equal to the mean difference between summer Ku-band backscatter and summer C-band backscatter PR during the five years with overlapping data (1999-2000 for ERS and QuikSCAT, and 2007-2009 for QuikSCAT and ASCAT). We use this intercalibration to develop time series plots for visual inspection in figures below, but not for inclusion in the dataset.

Multi-sensor backscatter at invariant non-urban sites.
Large expanses of continuous tropical rainforest land cover have been extensively used to validate the calibration of ERS, QuikSCAT, and ASCAT scatterometers because of the large-scale uniformity in the backscatter response from this vegetation [36][37][38] . We selected four tropical evergreen forest test sites ( Table 2) that we expect to have had minimal land-use/land-cover change during 1993-2020, based on location and a visible review of Google Earth image records. Sites were selected so as to exclude large water bodies or coastal grid cells. All four sites are in the southern hemisphere, so we used Jan-Feb-Mar for mean summer backscatter. We constructed a multi-sensor time series for each site by using the summer mean backscatter for each 0.05° grid cell, and then computing the aggregate mean and standard deviation for an 11 × 11 set of grid cells at each site (roughly 3500 km 2 ).
QuikSCAT Ku-band tropical evergreen forest backscatter PR is generally 0.02-0.05 lower than ERS and ASCAT C-band tropical evergreen forest backscatter (Fig. 2); this corresponds to roughly 0.7 dB to 1.3 dB lower σ° values, and is due primarily to the difference in sensor frequency/wavelength. For each site, we computed a simple Ku-band to C-band intercalibration offset as the mean difference between the five summer seasons with overlap ( www.nature.com/scientificdata www.nature.com/scientificdata/ tropical forest backscatter signal is generally stable over 1993-2020, and the constant offset QuikSCAT off generates a rather constant backscatter if QuikSCAT + offset is combined with ERS and ASCAT (Fig. 2). For the  Table 2 for site locations). For the QuikSCAT data, a simple Ku-band to C-band offset is computed for each site as the mean difference over the 5 overlapping years (1999)(2000)(2007)(2008)(2009) and QuikSCAT + offset is also plotted. Each point includes a standard deviation range for the 121 grid cells (0.05° lat/lon); in all cases this range is smaller than the symbol size. ERS backscatter data were missing for Jan-Mar 1994 at two sites. Linear fits (backscatter vs. year) are computed separately for ERS, QuikSCAT, and ASCAT data; trends (yr −1 ) are reported below the data points. Note: y-axis scale matches the y-axis scales of Figs. 3-6 below. Summer ASCAT backscatter compared to building data. Mathews et al. 16 reported validation results comparing QuikSCAT Ku-band backscatter to lidar-derived building height for nine US cities, ranging in area (of lidar data coverage) from 70 km 2 (Atlanta) to 8297 km 2 (Washington DC). For each city, they had a single-year lidar snapshot of building height, and selected QuikSCAT data from that same year. QuikSCAT data were processed with the Dense Sampling Method 14 to generate annual mean backscatter at 1-km resolution, and lidar data were aggregated to the same 1-km grid. Resulting coefficients of association strength (R 2 ) ranged from 0.04 (significant at p-value < 0.05) to 0.32 (significant at p-value < 0.01). Both QuikSCAT and lidar data were then converted to spatial trends by fitting polynomial functions over each city, generating a broad, smooth oblong domed shape for each city, elliptical in plan view with major and minor axis length differences. These trended datasets were more strongly associated, with R 2 values ranging from 0.33 to 0.98 (all significant with p-values < 0.01).
We compared 2015 summer mean ASCAT C-band backscatter to a continental-scale data set of building volume and building height 39 , which used random forest machine learning, with multiple remote sensing and other spatial input data sets (e.g., Landsat, MODIS, Sentinel-1 SAR, DEM, roads) to generate 1-km gridded data sets of c.2015 building height (m) and building volume (10 5 m 3 km −2 ) for urban areas across China, the USA, and Europe (Russia, Ukraine, and Belarus were not included in the building dataset). The random forest model was fit using a subset of available collections of lidar data, and tested against lidar data withheld from the fitting 39 . We used the results of the 'combined' model, where the models of building height, density, and volume are generated using data aggregated from all three regions in (China + USA + Europe); results for individual models of China, USA, Europe were similar 39 . These 1-km gridded building dimensional data were aggregated to 0.05° × 0.05°. We compared the building volume and height data to ASCAT Jul-Sep mean backscatter for 215 large cities (population >1 M [ref. 2 ]) in the three regions, extracting backscatter and building data for 11 × 11 grids of 0.05° grid cells for each city (roughly 2000-3500 km 2 , depending on latitude). Following Matthews et al. 16 , the building dimensional data were further smoothed, using a 5 × 5 grid moving mean window.
Applying a minimum 2014 built fraction threshold of 20% [refs. 2,33 ], there were 8450 urban grid cells (0.05°) across the 215 cities in China, Europe, and the USA that were used for comparison with the Li et al. 39 building metrics data; this increased to 11,548 grid cells with a lower built fraction threshold of 10% (Table 3). Correlations between building volume and C-band backscatter were strong ( Fig. 3; Table 3), with all significant at p < 0.001. Lowering the built fraction threshold to 10% led to a small increase in the correlation coefficients. Correlations between building height and ASCAT C-band backscatter were slightly weaker (Table 3), and again all significant at p < 0.001. In general, backscatter was lower for USA urban grid cells than for urban grid cells in China or Europe with similar building volumes (Fig. 3), as were the linear fit slopes (Table 3).

Usage Notes
Spatio-temporal data limitations. Within the overall land domain (+64.5° to −58°N, +180 to −180°E), The urban backscatter signal from scatterometers is affected by urban land change and densification. The grid does not resolve variations on the sub 1-km scale. As a result, the spatial domain constraints allow the data to be used on the WGS-84 standard coordinate system, as well as other coordinate systems, like GCJ-02 and BD-09, with minimal concerns.
This urban backscatter data set has been developed to investigate multi-decadal trends in urban growth, which for most cities over 1993-2020 has been essentially monotonically increasing. In order to filter out www.nature.com/scientificdata www.nature.com/scientificdata/ short-term variability in urban backscatter due to factors like vegetation seasonality, precipitation and surface wetting, freeze-thaw 15 , we have developed a three-month mean backscatter time series data set, and would recommend using one specific three-month period, e.g., the summer period, to construct an annual time series of change, as presented in Figs. 2, 4 and 5, and as used to compare to building volume (Fig. 3, Table 3) and building height (Table 3). To restrict the data to urban land, in the Seasonal_Urban_sig0_dB dataset, we excluded grid cells with <20% built fraction in 2014. As shown in Figs. 3-5 and Table 3, using a less restrictive built-fraction mask of <10% generated similar results. Using the 20% built fraction threshold on the GHSL coverage for 2000 or 1990 would have included 14% or 24% fewer grid cells globally, respectively. In our city-scale summary of the data below we selected urban grid cells within an 11 × 11 grid (0.05° cells, so roughly 50 km x 50 km, depending on latitude) centered on large cities, to minimize the influence of sub-urban and rural land outside the cities.
To allow users to experiment with different urban masks, we also have generated an unmasked land data set for each sensor (e.g., {sensor}_seasonal_Land_sig0_mean.nc). To allow users to explore different questions about www.nature.com/scientificdata www.nature.com/scientificdata/ urban backscatter seasonality with different temporal aggregations, we also have generated a monthly unmasked land data set for each sensor (e.g., {sensor}_monthly_land_sig0_mean.nc).
There is a difference in magnitude between C-band vs. Ku-band urban backscatter. We computed offsets for invariant tropical evergreen forest sites (Fig. 2) and major cities (e.g., Figs. 4 & 5 below); the offset magnitude varied from site to site, and no clear pattern was evident when this city-scale offset was mapped globally. However, as both the invariant sites and example cities show, a simple local offset can be computed that generates a fairly consistent overlapping 28-year time series. Inter-sensor differences are more likely due to urban backscatter differences caused by sensor geometry and wavelength differences than to changes in the urban structure from decade to decade. We do not consider the offset QuikSCAT backscatter that we computed to be a data product, and use it only to better illustrate the data. We do not recommend combining ERS and QuikSCAT offset and ASCAT into a single variable time series until a more rigorous intercalibration is done; instead, we recommend that each sensor's time series should be evaluated independently, though trends across the three sensors/ eras should be intercomparable. We also do not recommend quantitative intercomparison between particular www.nature.com/scientificdata www.nature.com/scientificdata/ cities until more research is done on the impact of urban surface properties on backscatter strength; instead, we recommend evaluating temporal trends in backscatter for individual large cities or aggregated to large regions.
Urban applications. Highly-built urban landscapes have much higher backscatter than evergreen tropical forests -compare Fig. 2 to Figs. 4 & 5 below -despite evergreen broadleaf forests having higher backscatter than other vegetated land cover types 40 . In addition, the change in urban backscatter over a decade, particularly QuikSCAT in the 2000s and ASCAT in the 2010s (Figs. 4 & 5), can be much larger than variation or trends in evergreen tropical forests (Fig. 2), indicating that urban trends are not due to instrument drift, but rather to changes in urban surface characteristics.
A 10-m resolution model of building height in German cities, using Sentinel-1 SAR data, under-predicts the number of buildings with heights >20-30 m, and appears to have a saturation effect at about 20 m [ref. 13 ]. The relationship of scatterometer backscatter to building volume doesn't seem to saturate, even for mega-cities in China (Fig. 2). This lack of saturation in the backscatter data may be due to a spatial averaging effect on the complicated nature of microwave backscatter from the built environment 12 , when reconstructing signals at ~10-km spatial resolution (urban districts) vs. 10-m resolution (individual buildings). We found a stronger linear correlation between 2015 ASCAT backscatter and building volume (Fig. 3) when backscatter values were in power return ratio, PR = 10^(σ 0 /10), where σ 0 is the backscatter in dB, than the relationship between building volume and backscatter σ 0 in dB. The data sets are posted as backscatter σ 0 in dB, but our analysis figures and tables use backscatter PR.
As an example of data usage, time series of summer mean urban backscatter 1993-2020, aggregated to individual large cities were generated for 12 large cities, and show a range of trends in urban growth at the city scale. For each city, an 11 × 11 grid of 0.05° lat/lon grid cells was selected, masked to remove grid cells with open water fraction >50% and/or built fraction in 2014 <20% (or <10%, for comparison) and a city-wide summer mean backscatter was computed for each year and sensor (Figs. 4 & 5). To reduce the influence of sub-urban and rural land outside the city and to be consistent with our earlier work 2,18 we restricted the domain of each city to an 11 × 11 grid. We note that neither the urban nor the all-land data sets posted at SEDAC are masked by distance from a city center, so different urban extents can be evaluated in future research.
The lower BF threshold (10%) includes a higher number of grid cells in almost all cases (Figs. 4 & 5). Differences between the two sets of panels in Figs. 4 and 5 (BF min = 20% or BF min = 10%) are small, though the lower threshold generally has slightly lower means and slightly higher variance across a city. There are clear differences between cities in the rates and timing of urban backscatter change over 1993-2020, although all of the example cities show mostly monotonic increase except Aleppo, Syria (Fig. 5), where backscatter dropped from 2012-2014 and had not recovered by 2020, consistent with a drop in night time lights in Aleppo from 2012-2015 resulting from the Syrian Civil War 41 .
The validation and urban time series analyses presented here were restricted to 11 × 11 blocks of the 0.05° × 0.05° grids (~2000-3500 km 2 ), centered on large cities (population >1 M), following Mahtta et al. 2 Microwave backscatter resolution is relatively coarse, though signal processing can sacrifice temporal resolution to improve spatial resolution 14,30 . We have targeted data for quantifying multi-decadal, global urban change at the scale of large cities (e.g., Figs. 4 & 5) to large regions. We caution against using these data sets to address questions about small cities (one to a few 0.05° grid cells, scale ~ 100 km 2 ), or detailed analysis of spatial patterns within a single city.
Urban backscatter will be affected by a number of structural and architectural factors that vary across the world's cities -for example, building materials, angular vs. rounded architecture, and the urban road network layout (gridded vs. 'random' 15 ). Sufficient granular data (i.e., global at less than 5-10 km resolution) are not available to resolve the impact of these effects. This variation will contribute to the scatter shown in Fig. 3, and makes it difficult to conduct detailed intercomparisons between cities. Until this variability is better studied and understood, we recommend that these urban backscatter data be used for regional-scale analyses, assessments of individual cities over time, and conclusions be confined to general patterns.
The overall relationship between ASCAT backscatter and building volume was quite different for the USA (56 large cities) than for China (113 large cities) or Europe (48 large cities), with USA cities having a much lower increase in backscatter per increase in building volume (Fig. 3). Comparison of backscatter to building height was similarly different for the USA (Table 3). Understanding what this difference implies about the urban built environment is an open research question. Looking at a few individual cities in the USA (Fig. 6), the backscatter-volume relationship for New York City is similar to the fit to all regions (see Fig. 3a above), while the relationships for Los Angeles and Washington DC are more representative of the average USA relationship. Some inter-city differences in backscatter may be due to differences in the surrounding environment, e.g., built sprawling suburbs, un-built arid or mountainous or forested or cropped land, or open water. The magnitude of these effects will depend on the degree of backscatter signal contribution from the surrounding environment to the selected urban grid cells. (2022) 9:88 | https://doi.org/10.1038/s41597-022-01193-w www.nature.com/scientificdata www.nature.com/scientificdata/ The combination of high resolution sensors and increasing capabilities to process large data sets should lead to higher resolution global urban structure data sets than these scatterometer data provide, for example, the SAR-based map of building height at 10-m resolution for Germany 13 . Since SAR data from Sentinel-1 is not available for the 1990s or 2000s, a multi-decadal building height time series from these SAR data cannot be developed until another decade of data are collected. Scatterometer data can provide an important prequel to these new SAR-based building data being developed, with global coverage for several decades of rapid urban growth, though further research would be needed to understand their relationships. This scatterometer data set will remain an important global urban built structure data set for the 1990-2020 era, a period of very rapid urban growth.

Code availability
Code used in this paper is available in the following locations: The github repository, tmilliman/sir_to_netcdf, (https://github.com/tmilliman/sir_to_netcdf) includes the python and bash scripts that: 1. Convert NASA SCP backscatter SIR images to NetCDF files of seasonal mean and standard deviation backscatter at 0.05° (lat/lon) for all land, and with an urban mask. Separate code for each sensor (ERS, QuikSCAT, ASCAT).
3. Create using the scripts in #2 CSV files with the mean backscatter for city-level grids around city centers and for also for the invariant regions shown in Fig. 3.
The github repository sfrolking/urban_backscatter_ERS_QSCAT_ASCAT (https://github.com/sfrolking/ urban_backscatter_ERS_QSCAT_ASCAT) includes R scripts that: 4. Evaluate seasonal backscatter for invariant evergreen tropical forest sites and construct Fig. 2. 5. use the CSV files from #3 above and correlate 2015 summer mean ASCAT backscatter with building volume data and construct Fig. 3. 6. use the CSV files from #3 above to generate annual mean summer backscatter time series plots for sample cities and construct Figs. 4-6.